According to Variety, Yates is currently in negotiations to handle at least the first instalment of the new series, which is very loosely based on Rowling's universe expanding textbook about magical creatures, and set in the same world as Harry Potter and friends. It will feature creatures and characters both new and familiar to Potter fans and, promises Rowling, will be "neither a prequel nor a sequel to the Harry Potter series, but an extension of the wizarding world" that takes place 70 years before Harry sets foot in the Great Hall in Hogwarts. That puts the setting somewhere around 1921, when Magizoologist and credited author of the book Newt Scamander would have been about 24 according to in-world chronology.
Yates is currently shooting Tarzan for the studio and appears ready to jump straight from that on to Fantastic Beasts next year. Given that he directed four Harry Potters on the trot with barely a break, if anyone can handle those production logistics, it's certainly Yates.
And let's face it – who else would Warner Bros entrust besides a man who directed four of the Potter movies, including the final two Harry Potter And The Deathly Hallows instalments? Now we'll just have to wait and see if the deal falls into place. As always, watch this space.